Some properties of the two-point functions in a dilatationally covariant field theory

The object of our concern are some properties of the two-point functions in a model of dilatationally covariant field theory. We examine the one- and two-dimensional irreducible representations of the dilatation group. For the one-dimensional case we obtain either a massless free field theory or a theory of an interacting field which does not contribute on the mass shell μ=p²=0 and is characterized by a spectral function μ^r₊?1. In the two-dimensional case both fields differ from the free field, their spectral functions ρ_ij(μ) do not vanish identically and are products of two factors, a polynomial of order up to two in ln μ and μ^r₊?-1. The differences between the case of internal symmetry and the case of dilatations are emphasized. The formula for the form factor in the Araki-Haag limit is given.     

On the structure of the conformal covariant N-point functions

The conformal covariant n-point functions for the fields with arbitrary spin and scale dimension are found. These functions are determined up to a set of arbitrary functions on $\text{n(n?3)}\text{2}$ independent conformal invariant variables. These arbitrary functions cannot be determined without dynamical assumptions.     

Structure of the two-point green function of the gauge field for N = 1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives

For the most general renormalizable N = 1 supersymmetric Yang-Mills theory, regularized by higher derivatives, we investigate a contribution to the Gell-Mann-Low function from the two-loop diagrams, containing cubic interaction of the matter superfields. We find that all integrals with respect to the loop momentum in the massless case are factorized to the integrals of total derivatives and can be easily calculated. Thus, we explain the origin of the relation between the two-loop β-function and the one-loop anomalous dimension of the matter superfield.     

Light cone structure of the current two-point function and asymptotic behaviour in momentum space

We prove the correspondence between the degree of singularity of a two point function on the light cone and the asymptotic behaviour of its Fourier transform. The result is relevant for e⁺?e^? annihilation.     

On the covariant formulation of quantum mechanics

We give picture-covariant formulations of the equations of motion for observables and states such that the Hamiltonian operator is transformed asH-0304;=U(t)HU (t) under a time-dependent unitary transformationU(t). Next, we consider the explicit and implicit covariance of Heisenberg's equations of motion for observables with respect to general transformations of coordinate operators. Most of our representation is spread out over a number of textbooks and articles, where the subject has been considered with greater or lesser clarity from different points of view.     

The massless two-loop two-point function

We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter . As a side product, we show that in the Laurent expansion of the two-loop integral only rational numbers and multiple zeta values occur. Our method of calculation obtains the two-loop integral as a convolution product of two primitive one-loop integrals. We comment on the generalization of this product structure to higher loop integrals.Received: 1 September 2003, Revised: 30 September 2003, Published online: 12 November 2003     

On the covariant description of wavefunction collapse

The instantaneous change of the wavefunction known as the “collapse” of the wavefunction leads to ambiguities in relativistic quantum mechanics. It is here shown that a relativistically satisfactory generalization follows from the treatment of the measurement as a physical interaction.     

On the calculation of the two-point function for the thirring-model by the method of functional integration

By the method of functional integration the two-point functionS _F for the spinor model with the interaction\( - \lambda (\bar \psi \psi )^2 \) is calculated in a two-dimensional space-time. After Fourier-transformationS _F (p) results as a power series with respect to 1/√λ. If we change the order of terms, we get a series in powers of γp. Each coefficient is a series in powers of 1/√λ. The first terms of this series are considered as a good approximation for bigλ. By reasons of convergence of the integrals we must displace the expansion centre of the series in powers ofγ p fromp ²=0 top ²=a ².     

On the Berkovits covariant quantization of GS superstring

We study the covariant quantization of the Green–Schwarz (GS) superstrings proposed recently by Berkovits. In particular, we reformulate the Berkovits approach in a way that clarifies its relation with the GS approach and allows to derive in a straightforward way its extension to curved spacetime background. We explain the procedure working explicitly in the case of the heterotic string.     

Nearest-neighbor two-point correlation function of the Z-invariant eight-vertex model

The nearest-neighbor two-point correlation function of the Z-invariant inhomogeneous eight-vertex model in the thermodynamic limit is computed using the free-field representation. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 243–247 (10 August 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The two-point correlation function of the one-dimensional matrix model

Following Kostov and Ben-Menahem, we calculate the two-puncture correlation function for the one-dimensional matrix model. We find that it depends on the details of discretization for all momenta p. Its only universal features are its vanishing as p → 0 and the appearance of double poles at |p| = n/√′, N = 1,2,…. We show how to derive these double poles in the conformal gauge treatment of Liouville gravity.     

On conformally covariant spinor field equations

A spinor field equation, covariant with respect to the general conformal group (including reflections), should consist in general of not less than eight linear equations and then, in Minkowski space, could be represented by not less than two massless Dirac equations. Their reduction through projectors to only one equation, while not spoiling conformal covariance implies unphysical consequences. It is shown instead that two Dirac equations may be brought unambiguously through a stereographic projection to a manifestly conformal covariant form inE _4,2 space. The physical implications are discussed and it is shown that if the fundamental elementary interactions are expressed in terms of conformal semispinors (which can never appear as free particles), then the corresponding physical Dirac spinors appear in the elementary interactions in terms of their chiral projections. This could indicate both the conformally invariant origin of weak interactions and their fundamental character. The possibility of constructing unified models from conformally invariant Lagrangians is envisaged.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.A preliminary version was issued as Internal Report IC/78/43, ICTP Trieste May 1978, see also Lett. Nuovo Cim.21 (1978), 473.I am indebted to Prof. I. T.Todorov for interesting discussions.     

Two-particle correlations in the wave function and covariant current approaches

We consider two-particle correlations which appear in relativistic nuclear collisions owing to the quantum statistics of identical particles in the frame of two formalisms: wave-function and current parametrizations. The first one is based on solution of the Cauchy problem, whereas the second one is a so-called current parametrization of the source of secondary particles. We argue that these two parametrizations of the source coincide when the wave-function at freeze-out times is put into a specific correspondence with a current. Then, the single-particle Wigner density evaluated in both approaches gives the same result. The text was submitted by the authors in English.     

The photon two-point function in unitary approximation

The photon two-point function is calculated using the exponential representation for the time-evolution operator taking into account terms up to second order ine in the exponent. The limiting case of vanishing electron mass is examined and it is shown that mass singularities cancel by means of unitarity. Near mass shell the causal Green function exhibits in the limit of vanishing electron mass the expected cut behaviour, off mass shell we recover the result of the usual perturbation theory.     

New symmetries and ghost structure of covariant string theories

It is shown that there exists an infinite set of new symmetries of the previously given covariant string formulations. These symmetries have themselves an infinite set of hidden local symmetries and so on. A new physically equivalent further extended string action is given in which the infinite set of symmetries is most easily displayed. A quantization involving gauge fixing and ghosts of the various covariant string actions is given.     

On the dilaton vertex in the covariant formulation of strings

We investigate the dilaton vertex operator in the covariant formulation of strings. We find that the Faddeev-Popov ghosts play an essential role to construct conformal fields.